skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quasi-static capacitance of a weakly compensated semiconductor with hopping conduction (on the example of p-Si:B)

Abstract

A moderately doped semiconductor is considered on the insulator side of the insulator-metal phase transition, where the acceptors in (-1), (0), and (+1) charge states form A{sup 0} and A{sup +} bands. The expressions are derived for the Debye-Hueckel and Schottky-Mott screening lengths of an external electrostatic field for the case of hopping transport of holes via acceptors. The quasistatic capacitance of a semiconductor is calculated in the temperature region where hopping hole conductances in the A{sup 0} and A{sup +} bands are approximately equal. It is shown that the Debye-Hueckel screening length can be determined using the measurements of quasistatic capacitance even in the high-field regime, i.e., in the Schottky-Mott approximation. The frequency of an electric signal in the measurements of quasistatic semiconductor capacitance in a metal-insulator-semiconductor structure must be much lower than the average frequency of hole hopping via acceptors (boron atoms in silicon)

Authors:
;  [1];  [2]
  1. Belarusian State University (Belarus)
  2. Russian Academy of Sciences, Ioffe Physicotechnical Institute (Russian Federation)
Publication Date:
OSTI Identifier:
21088464
Resource Type:
Journal Article
Resource Relation:
Journal Name: Semiconductors; Journal Volume: 41; Journal Issue: 1; Other Information: DOI: 10.1134/S1063782607010083; Copyright (c) 2007 Nauka/Interperiodica; Article Copyright (c) 2007 Pleiades Publishing, Ltd; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; BORON; CAPACITANCE; CHARGE STATES; DOPED MATERIALS; HOLES; PHASE TRANSFORMATIONS; SEMICONDUCTOR MATERIALS; SILICON

Citation Formats

Poklonski, N. A., E-mail: poklonski@bsu.by, Vyrko, S. A., and Zabrodskii, A. G.. Quasi-static capacitance of a weakly compensated semiconductor with hopping conduction (on the example of p-Si:B). United States: N. p., 2007. Web. doi:10.1134/S1063782607010083.
Poklonski, N. A., E-mail: poklonski@bsu.by, Vyrko, S. A., & Zabrodskii, A. G.. Quasi-static capacitance of a weakly compensated semiconductor with hopping conduction (on the example of p-Si:B). United States. doi:10.1134/S1063782607010083.
Poklonski, N. A., E-mail: poklonski@bsu.by, Vyrko, S. A., and Zabrodskii, A. G.. Mon . "Quasi-static capacitance of a weakly compensated semiconductor with hopping conduction (on the example of p-Si:B)". United States. doi:10.1134/S1063782607010083.
@article{osti_21088464,
title = {Quasi-static capacitance of a weakly compensated semiconductor with hopping conduction (on the example of p-Si:B)},
author = {Poklonski, N. A., E-mail: poklonski@bsu.by and Vyrko, S. A. and Zabrodskii, A. G.},
abstractNote = {A moderately doped semiconductor is considered on the insulator side of the insulator-metal phase transition, where the acceptors in (-1), (0), and (+1) charge states form A{sup 0} and A{sup +} bands. The expressions are derived for the Debye-Hueckel and Schottky-Mott screening lengths of an external electrostatic field for the case of hopping transport of holes via acceptors. The quasistatic capacitance of a semiconductor is calculated in the temperature region where hopping hole conductances in the A{sup 0} and A{sup +} bands are approximately equal. It is shown that the Debye-Hueckel screening length can be determined using the measurements of quasistatic capacitance even in the high-field regime, i.e., in the Schottky-Mott approximation. The frequency of an electric signal in the measurements of quasistatic semiconductor capacitance in a metal-insulator-semiconductor structure must be much lower than the average frequency of hole hopping via acceptors (boron atoms in silicon)},
doi = {10.1134/S1063782607010083},
journal = {Semiconductors},
number = 1,
volume = 41,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}
  • Using uniaxial stress to tune the critical density near that of the sample, we have studied in detail the low-temperature conductivity of p-type Si:B in the insulating phase very near the metal-insulator transition. For all values of temperature and stress, the conductivity collapses onto a single universal curve, {sigma}(S,T)=AT{sup 1/2}F[T{sup {asterisk}}(S)/T]. For large values of the argument, the scaling function F[T{sup {asterisk}}(S)/T] is well fit by exp[{minus}(T{sup {asterisk}}/T){sup 1/2}], the exponentially activated form associated with variable-range hopping when electron-electron interactions cause a soft Coulomb gap in the density of states at the Fermi energy. The temperature dependence of the prefactor,more » corresponding to the T dependence of the critical curve, has been determined reliably for this system, and is {proportional_to}T{sup 0.5}. We show explicitly that neglecting the prefactor leads to substantial errors in the determination of the T{sup {asterisk}}{close_quote}s and the critical exponents derived from them. The conductivity is not consistent with Mott variable-range hopping, exp[{minus}(T{sup {asterisk}}/T){sup 1/4}], in the critical region, nor does it obey this form for any range of the parameters. Instead, the conductivity of Si:B is well fit by {sigma}=AT{sup 1/2}&hthinsp;exp[{minus}(T{sup {asterisk}}/T){sup {alpha}}] for smaller argument of the scaling function, with {alpha}=0.31 related to the critical exponents of the system at the metal-insulator transition. {copyright} {ital 1999} {ital The American Physical Society}« less
  • The electrostatic model of ionization equilibrium between hydrogen-like acceptors and v-band holes in crystalline covalent p-type semiconductors is developed. The range of applicability of the model is the entire insulator side of the insulator–metal (Mott) phase transition. The density of the spatial distribution of acceptor- and donor-impurity atoms and holes over a crystal was assumed to be Poissonian and the fluctuations of their electrostatic potential energy, to be Gaussian. The model takes into account the effect of a decrease in the energy of affinity of an ionized acceptor to a v-band hole due to Debye–Hückel ion screening by both freemore » v-band holes and localized holes hopping over charge states (0) and (–1) of acceptors in the acceptor band. All donors are in charge state (+1) and are not directly involved in the screening, but ensure the total electroneutrality of a sample. In the quasiclassical approximation, analytical expressions for the root-mean-square fluctuation of the v-band hole energy W{sub p} and effective acceptor bandwidth W{sub a} are obtained. In calculating W{sub a}, only fluctuations caused by the Coulomb interaction between two nearest point charges (impurity ions and holes) are taken into account. It is shown that W{sub p} is lower than W{sub a}, since electrostatic fluctuations do not manifest themselves on scales smaller than the average de Broglie wavelength of a free hole. The delocalization threshold for v-band holes is determined as the sum of the diffusive-percolation threshold and exchange energy of holes. The concentration of free v-band holes is calculated at the temperature T{sub j} of the transition from dc band conductivity to conductivity implemented via hopping over acceptor states, which is determined from the virial theorem. The dependence of the differential energy of the thermal ionization of acceptors at the temperature 3T{sub j}/2 on their concentration N and degree of compensation K (the ratio between the donor and acceptor concentrations) is determined. Good quantitative agreement between the results of the calculation and data on the series of neutron transmutation doped p-Ge samples is obtained up to the Mott transition without using any fitting parameters.« less
  • Low-frequency electrical capacitance of silicon crystals in the case of hopping migration of both electrons and bipolarons (electron pairs) via the defects of one type, which stabilizes the Fermi level near the midgap, is calculated. The crystals with two-level defects in three charge states (+1, 0, or -1) with a negative correlation energy are considered. It is shown that, as the absolute value of the external potential is increased, the capacitance of silicon containing defects with positive correlation energy increases, while that with defects with negative correlation energy decreases. The expression for the drift and diffusion components of current densitymore » for bipolarons hopping from defects with the charge state -1 to defects with the charge state +1 was derived for the first time.« less
  • Capacitance nonlinearities were studied in atomic layer deposited HfO{sub 2} films using two types of signals: a pure ac voltage of large magnitude (ac nonlinearities) and a small ac voltage superimposed to a large dc voltage (dc nonlinearities). In theory, ac and dc nonlinearities should be of the same order of magnitude. However, in practice, ac nonlinearities are found to be an order of magnitude higher than dc nonlinearities. Besides capacitance nonlinearities, hopping conduction is studied using low-frequency impedance measurements and is discussed through the correlated barrier hopping model. The link between hopping and nonlinearity is established. The ac nonlinearitiesmore » are ascribed to the polarization of isolated defect pairs, while dc nonlinearities are attributed to electrode polarization which originates from defect percolation paths. Both the ac and dc capacitance nonlinearities display an exponential variation with voltage, which results from field-induced lowering of the hopping barrier energy.« less
  • Measurements of the electron and hole drift mobilities and the optical-absorption edge in compensated hydrogenated amorphous silicon are reported. The mobilities of both carriers decrease with increasing doping and converge to similar values for gas-phase doping levels greater than one part per thousand. The mobility and optical-absorption data are not consistent with disorder-induced band-tail broadening, but agree with the predictions of a model of long-range potential fluctuations originating from charged donor and acceptor states.